Select outer layer of hollow object
If you are using a Solidify modifier, you can't select the 'virtual' geometry generated by the modifier separately until it is applied.



The faces coloured in orange here are the real geometry, and the grey faces are 'virtual' geometry, this can't be selected separately. If you want to do something with the outer or inner layer you will need to Apply the modifier, that makes all geometry of that object 'real'.